%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SEU527^2 : TPTP v9.2.0. Released v3.7.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n001.cluster.edu % Model : x86_64 x86_64 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz % Memory : 8042.1875MB % OS : Linux 3.10.0-693.el7.x86_64 % CPULimit : 300s % WCLimit : 300s % DateTime : Fri Oct 3 08:01:50 PM UTC 2025 % Result : Theorem 3.57s 3.80s % Output : Proof 3.65s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.12 % Problem : SEU527^2 : TPTP v9.2.0. Released v3.7.0. % 0.07/0.13 % Command : duper %s % 0.14/0.34 % Computer : n001.cluster.edu % 0.14/0.34 % Model : x86_64 x86_64 % 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.14/0.34 % Memory : 8042.1875MB % 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.14/0.34 % CPULimit : 300 % 0.14/0.34 % WCLimit : 300 % 0.14/0.34 % DateTime : Fri Oct 3 05:58:38 EDT 2025 % 0.14/0.35 % CPUTime : % 3.57/3.80 SZS status Theorem for theBenchmark.p % 3.57/3.80 SZS output start Proof for theBenchmark.p % 3.57/3.80 Clause #0 (by assumption #[]): Eq (Eq emptysetE (∀ (Xx : Iota), in Xx emptyset → ∀ (Xphi : Prop), Xphi)) True % 3.57/3.80 Clause #1 (by assumption #[]): Eq % 3.57/3.80 (Eq setadjoinE % 3.57/3.80 (∀ (Xx A Xy : Iota), in Xy (setadjoin Xx A) → ∀ (Xphi : Prop), (Eq Xy Xx → Xphi) → (in Xy A → Xphi) → Xphi)) % 3.57/3.80 True % 3.57/3.80 Clause #2 (by assumption #[]): Eq (Not (emptysetE → setadjoinE → ∀ (Xx Xy : Iota), in Xx (setadjoin Xy emptyset) → Eq Xx Xy)) True % 3.57/3.80 Clause #3 (by clausification #[0]): Eq emptysetE (∀ (Xx : Iota), in Xx emptyset → ∀ (Xphi : Prop), Xphi) % 3.57/3.80 Clause #18 (by clausification #[1]): Eq setadjoinE % 3.57/3.80 (∀ (Xx A Xy : Iota), in Xy (setadjoin Xx A) → ∀ (Xphi : Prop), (Eq Xy Xx → Xphi) → (in Xy A → Xphi) → Xphi) % 3.57/3.80 Clause #22 (by clausification #[2]): Eq (emptysetE → setadjoinE → ∀ (Xx Xy : Iota), in Xx (setadjoin Xy emptyset) → Eq Xx Xy) False % 3.57/3.80 Clause #23 (by clausification #[22]): Eq emptysetE True % 3.57/3.80 Clause #24 (by clausification #[22]): Eq (setadjoinE → ∀ (Xx Xy : Iota), in Xx (setadjoin Xy emptyset) → Eq Xx Xy) False % 3.57/3.80 Clause #25 (by backward demodulation #[23, 3]): Eq True (∀ (Xx : Iota), in Xx emptyset → ∀ (Xphi : Prop), Xphi) % 3.57/3.80 Clause #30 (by clausification #[25]): ∀ (a : Iota), Eq (in a emptyset → ∀ (Xphi : Prop), Xphi) True % 3.57/3.80 Clause #31 (by clausification #[30]): ∀ (a : Iota), Or (Eq (in a emptyset) False) (Eq (∀ (Xphi : Prop), Xphi) True) % 3.57/3.80 Clause #32 (by clausification #[31]): ∀ (a : Iota) (a_1 : Prop), Or (Eq (in a emptyset) False) (Eq a_1 True) % 3.57/3.80 Clause #33 (by clausification #[24]): Eq setadjoinE True % 3.57/3.80 Clause #34 (by clausification #[24]): Eq (∀ (Xx Xy : Iota), in Xx (setadjoin Xy emptyset) → Eq Xx Xy) False % 3.57/3.80 Clause #35 (by backward demodulation #[33, 18]): Eq True (∀ (Xx A Xy : Iota), in Xy (setadjoin Xx A) → ∀ (Xphi : Prop), (Eq Xy Xx → Xphi) → (in Xy A → Xphi) → Xphi) % 3.57/3.80 Clause #52 (by clausification #[34]): ∀ (a : Iota), Eq (Not (∀ (Xy : Iota), in (skS.0 6 a) (setadjoin Xy emptyset) → Eq (skS.0 6 a) Xy)) True % 3.57/3.80 Clause #53 (by clausification #[52]): ∀ (a : Iota), Eq (∀ (Xy : Iota), in (skS.0 6 a) (setadjoin Xy emptyset) → Eq (skS.0 6 a) Xy) False % 3.57/3.80 Clause #54 (by clausification #[53]): ∀ (a a_1 : Iota), Eq (Not (in (skS.0 6 a) (setadjoin (skS.0 7 a a_1) emptyset) → Eq (skS.0 6 a) (skS.0 7 a a_1))) True % 3.57/3.80 Clause #55 (by clausification #[54]): ∀ (a a_1 : Iota), Eq (in (skS.0 6 a) (setadjoin (skS.0 7 a a_1) emptyset) → Eq (skS.0 6 a) (skS.0 7 a a_1)) False % 3.57/3.80 Clause #56 (by clausification #[55]): ∀ (a a_1 : Iota), Eq (in (skS.0 6 a) (setadjoin (skS.0 7 a a_1) emptyset)) True % 3.57/3.80 Clause #57 (by clausification #[55]): ∀ (a a_1 : Iota), Eq (Eq (skS.0 6 a) (skS.0 7 a a_1)) False % 3.57/3.80 Clause #58 (by clausification #[35]): ∀ (a : Iota), % 3.57/3.80 Eq (∀ (A Xy : Iota), in Xy (setadjoin a A) → ∀ (Xphi : Prop), (Eq Xy a → Xphi) → (in Xy A → Xphi) → Xphi) True % 3.57/3.80 Clause #59 (by clausification #[58]): ∀ (a a_1 : Iota), % 3.57/3.80 Eq (∀ (Xy : Iota), in Xy (setadjoin a a_1) → ∀ (Xphi : Prop), (Eq Xy a → Xphi) → (in Xy a_1 → Xphi) → Xphi) True % 3.57/3.80 Clause #60 (by clausification #[59]): ∀ (a a_1 a_2 : Iota), Eq (in a (setadjoin a_1 a_2) → ∀ (Xphi : Prop), (Eq a a_1 → Xphi) → (in a a_2 → Xphi) → Xphi) True % 3.57/3.80 Clause #61 (by clausification #[60]): ∀ (a a_1 a_2 : Iota), % 3.57/3.80 Or (Eq (in a (setadjoin a_1 a_2)) False) (Eq (∀ (Xphi : Prop), (Eq a a_1 → Xphi) → (in a a_2 → Xphi) → Xphi) True) % 3.57/3.80 Clause #62 (by clausification #[61]): ∀ (a a_1 a_2 : Iota) (a_3 : Prop), % 3.57/3.80 Or (Eq (in a (setadjoin a_1 a_2)) False) (Eq ((Eq a a_1 → a_3) → (in a a_2 → a_3) → a_3) True) % 3.57/3.80 Clause #63 (by clausification #[62]): ∀ (a a_1 a_2 : Iota) (a_3 : Prop), % 3.57/3.80 Or (Eq (in a (setadjoin a_1 a_2)) False) (Or (Eq (Eq a a_1 → a_3) False) (Eq ((in a a_2 → a_3) → a_3) True)) % 3.57/3.80 Clause #64 (by clausification #[63]): ∀ (a a_1 a_2 : Iota) (a_3 : Prop), % 3.57/3.80 Or (Eq (in a (setadjoin a_1 a_2)) False) (Or (Eq ((in a a_2 → a_3) → a_3) True) (Eq (Eq a a_1) True)) % 3.57/3.80 Clause #66 (by clausification #[64]): ∀ (a a_1 a_2 : Iota) (a_3 : Prop), % 3.65/3.81 Or (Eq (in a (setadjoin a_1 a_2)) False) (Or (Eq (Eq a a_1) True) (Or (Eq (in a a_2 → a_3) False) (Eq a_3 True))) % 3.65/3.81 Clause #67 (by clausification #[66]): ∀ (a a_1 a_2 : Iota) (a_3 : Prop), % 3.65/3.81 Or (Eq (in a (setadjoin a_1 a_2)) False) (Or (Eq (in a a_2 → a_3) False) (Or (Eq a_3 True) (Eq a a_1))) % 3.65/3.81 Clause #68 (by clausification #[67]): ∀ (a a_1 a_2 : Iota) (a_3 : Prop), % 3.65/3.81 Or (Eq (in a (setadjoin a_1 a_2)) False) (Or (Eq a_3 True) (Or (Eq a a_1) (Eq (in a a_2) True))) % 3.65/3.81 Clause #70 (by superposition #[68, 56]): ∀ (a : Prop) (a_1 a_2 : Iota), % 3.65/3.81 Or (Eq a True) (Or (Eq (skS.0 6 a_1) (skS.0 7 a_1 a_2)) (Or (Eq (in (skS.0 6 a_1) emptyset) True) (Eq False True))) % 3.65/3.81 Clause #95 (by clausification #[57]): ∀ (a a_1 : Iota), Ne (skS.0 6 a) (skS.0 7 a a_1) % 3.65/3.81 Clause #96 (by clausification #[70]): ∀ (a : Prop) (a_1 a_2 : Iota), % 3.65/3.81 Or (Eq a True) (Or (Eq (skS.0 6 a_1) (skS.0 7 a_1 a_2)) (Eq (in (skS.0 6 a_1) emptyset) True)) % 3.65/3.81 Clause #97 (by forward contextual literal cutting #[96, 95]): ∀ (a : Prop) (a_1 : Iota), Or (Eq a True) (Eq (in (skS.0 6 a_1) emptyset) True) % 3.65/3.81 Clause #100 (by superposition #[97, 32]): ∀ (a a_1 : Prop), Or (Eq a True) (Or (Eq True False) (Eq a_1 True)) % 3.65/3.81 Clause #103 (by clausification #[100]): ∀ (a a_1 : Prop), Or (Eq a True) (Eq a_1 True) % 3.65/3.81 Clause #108 (by falseElim #[103]): ∀ (a : Prop), Eq a True % 3.65/3.81 Clause #109 (by falseElim #[108]): False % 3.65/3.81 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------